Universal countable-dimensional topological groups

We construct a separable metrizable countable-dimensional (respectively strongly countable-dimensional) abelian topological group that contains all countable-dimensional separable metrizable abelian topological absolute Gδ-groups (respectively all finite-dimensional separable metrizable abelian topological absolute Gδσ-groups). A similar result is proved for separable metrizable abelian topological group that are countable-dimensional with respect to integral cohomological dimension.